COMMON SURFACE OF TWO FLUIDS. 



15 



same horizontal plane, even though the continuity of the 

 surface be interrupted by the immersion of solid bodies. 

 // any number of vessels, containing the same 

 liquid, are in communication, the liquid stands at 

 the same height in each vessel. 



This sometimes appears under the form of the assertion 

 that liquids maintain their level. 



EEM. The construction by which towns are supplied 

 with water furnishes a practical illustration of this princi- 

 ple. Pipes, leading from a reservoir placed on a height, 

 carry the water, underground or over roads, to the tops of 

 houses or to any point provided that no portion of a pipe is 

 higher than the surface of the water in the reservoir. 



12. The Common Surface of Two Fluids. Let AD 



be the upper surface of the lighter fluid, and BO the com- 

 mon surface of the two fluids; AD is hori- 

 zontal (Art. 11). Let P and Q be two points 

 in the heavier liquid, both equally distant 

 from the surface AD, and therefore in the 

 same horizontal plane. Draw the vertical 

 lines Pa and QJ, meeting the common sur- 

 face of the fluids in c and d. Let w be the 

 weight of a unit of volume of the upper fluid, 

 and w' that of the lower. 

 Then we have 



A a 



B 





Fig. 7 



and 



" pressure at P = iv'-cP + w-ac', 

 pressure at Q = iv'-dQ, + w-bd. 



Since the pressures at P and Q are equal (Art. 11, Cor. 3), 

 they being in the same horizontal plane, we have 



w'-cP + W'ttc = w'-dQ, + W'bd. (1) 



But 



cP + ac = c7Q + bd 



